Provided the card and the cooler dosen't exceed 170mm or 17cm or 6.7" you'll be fine. Based on the specs of the case its accomodates full height PCI slot expansion cards therefore I don't see it being a problem. The height of the cooler is only a 104mm tall (vertically), so when you install it on the 4870 you'll have to consider any additional height based on its mounting position, but I don't see it being a problem.

Not to be a jackass and I am all about helping out where I can, just for future reference most information is available from the respective manufacturers website and will likely provide you the information you might be looking for.